Chapter 1 — Predicates and Individuals
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Before we can reason about the world, we need to decide what the world contains and what we want to say about it. Aristotelian logic is built on a single fundamental notion: the predicate. Individuals are special predicates.

1.1 Predicates

A predicate is a general term that expresses a property, a kind, or a category. Predicates can apply to other predicates, or to individuals.
Examples of predicates:
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• is mortal
• is a mammal
• is warm-blooded
• can fly
• is a bird
Notice that predicates can be nested: “every bird is a vertebrate” applies the predicate “is a vertebrate” to all things falling under “is a bird”. This is the normal case in Aristotelian logic: the subject of a judgment is itself a predicate.

1.2 Individuals

An individual is a limiting case of a predicate — one that applies to exactly one thing. Terms name predicates and singular terms name individuals. For example: “Socrates” names a predicate that picks out exactly one individual, Socrates.
Examples of individuals (as singular predicates):
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• Socrates (this particular person)
• This dog in front of me (this particular animal)
• The oak tree in my garden (this particular tree)
• A unique, particular triangle or number
In our formal model, both predicates and individuals are represented by the same set of numbers: 1, 2, 3, … up to n. Individuals are those numbers that are designated as “atomic” — they appear only on the subject side of judgments, never as predicates of others.

1.3 Partial Knowledge

Here is what makes Aristotelian logic philosophically distinctive: we do not need to know everything about all predicates and individuals. We only know what we have learned so far.
Imagine you are a naturalist exploring a new island. You have observed some animals and learned some things about them — but not everything. You have partial knowledge. Aristotelian logic lets you reason with exactly that partial knowledge, draw conclusions from it, and extend it step by step as you learn more.
This is fundamentally different from classical mathematical logic, which assumes a complete, determined `Tarskian World’ where every statement is either true or false. In Aristotle’s World, truth is something that accumulates through learning.

1.4 Your First World: An Example

Let us build a small world with three predicates and two individuals.
World: Animals on an Island
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Predicates: 1 = is a bird, 2 = can fly, 3 = lives in water
Individuals: 4 = penguin, 5 = eagle
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What do we know so far?
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• A penguin is a bird. (individual 4 falls under predicate 1)
• An eagle is a bird. (individual 5 falls under predicate 1)
• An eagle can fly. (individual 5 falls under predicate 2)
This is our starting point: three facts about two animals. Notice what we do NOT know yet: Can a penguin fly? Does a bird always live on land? and many other possible facts we have not mentioned. Aristotelian logic works with exactly this kind of partial knowledge.
In the next chapter, we will learn how to express these facts formally using the four Aristotelian judgment forms A, E, I, O.

Interactive: Build Your Own World

Move the sliders to choose how many predicates and individuals your world contains. The table shows all terms: predicates (P1, P2, ...) appear in both rows and columns; individuals (a1, a2, ...) appear in rows only.
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Individuals
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3 predicates (P1…P3) + 2 individuals (a1…a2)
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Reflection
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The rows show subjects (S), the columns show predicates (P). A filled cell would mean: “S falls under P”. Notice that individuals (a1, a2, …) appear as rows only — they cannot themselves be predicated of anything. Predicates (P1, P2, …) appear in both rows and columns.
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